A review of the rheo-optical properties of linear high polymers

Some principles ans laws, expressing the mechanical and optical behavior of linear viscoelastic materials, are reviewed. The mechanical properties of the polymers in the transition region may be represented by a condensed general method containing Ferry's modulus or compliance-reduction scheme, the time-temperature superposition principle and the Gauss error integral representation. The optical behavior of high polymers is expressed by the stress- and strain-optical coefficients in creep or relaxation, which relate birefringence to stresses or strains. It was recently shown experimentally that, instead of a pair of independent linear differential operator relations, which characterize the mechanical properties of the viscoelastic materials, only one operator relation is needed and the initial value of another at the glassy or rubbery state. Then, a single test is sufficient for the complete determination of the mechanical and optical viscoelastic behavior, provided the value of another elastic constant at the glassy or rubbery state is also determined and the variation of birefringence with time is simultaneously measured with the mechanical-characteristic quantities of the material.     

A photomechanics material for elastoplastic stress analysis

The object of this investigation was to develop a technique or method for elastoplastic stress analysis using the optical effects of transparent materials. Of paramount importance was the selection and characterization of a suitable model material. In particular, it was desirable that the material be able to undergo large plastic strains while, at the same time, exhibiting a suitable level of optical response. A mixture of flexible and rigid polyester resins was found suitable, i.e., the mixture exhibited large strains and good optical response. It was found that unload birefringence (fringe order immediately upon removal of load) could be used to determine strain for a uniaxial-stress field. In particular, it provided a means for evaluating stress- and strain-concentration factors. Comparisons with other methods showed that the proposed method was reliable and gave results that are similar to those by other means. The usefulness of the material and method for two- and three-dimensional problems awaits further study.     

Half-fringe photoelasticity: A new approach to whole-field stress analysis

This paper presents a new method for whole-field stress analysis based on a symbiosis of two techniques—classical photoelasticity and modern digital image analysis. The resulting method is called ‘half-fringe photoelasticity (HFP)’. Classical photoelasticity demands materials with high birefringence, which leads to extensive use of plastics as model materials. Since the behavior of these materials is often different from that of the prototype materials, their use distorts the similitude relationships. In many contemporary problems this distortion is untenable. HFP offers a way out of this dilemma. It permits materials and loads to be chosen so that no more than one half of a fringe order appears in the area of interest. Thus, for example, glass, which behaves linearly up to high stress levels and over a wide range of temperatures, could be used as model material. Alternatively, models from polymeric materials could be used under very low load in order to stay within the linear part of the stress-strain diagram and to prevent large deformations. The half-fringe-photoelasticity system, which is described here, utilizes the resulting low levels of birefringence for effective stress analysis. This paper describes the system. It outlines a calibration routine and illustrates its application to two simple problems using glass models.     

Characteristic relations of flow birefringence

This is the first of two closely related papers on the flow-birefringence response to the velocity vector field of a particular liquid representing a certain class of birefringent bodies.^* The flowing material under study was the aqueous solution of the compound known under the name NGS 1828 and commonly known as “milling yellow” or “acid yellow”. This solution appears to exhibit all three major mechanisms of birefringence. The physical parameters characterizing this material depend strongly on temperature, concentration and age and, therefore, it can be considered as representing a typical class of liquids used in flow-model experiments. The paper presents the experimental evidence that the flow birefringence cannot be explained and described by the simple mathematical model of birefringence in solid continuum which relates the changes of the components of dielectric tensor to the components of stress and strain tensors, or their derivatives, and which neglects the influence of the spectral frequency (wavelength of radiation). Results are presented for transmission birefringence (and for scattered-light birefringence in the second paper) in the visible and the infrared bands of radiation. It is shown that:

- the amount of birefringence depends strongly and non-monotonically on wavelength of radiation;

- the linear range of optical response to shear-strain rate depends on wavelengths of radiation;

- the directions of optic axes strongly depend both on the shear-strain rate and on the wavelength of radiation, even in the linear range of mechanical response.

It is further shown that there exists a relation between the absorption bands, the maximum transmittance, the dispersion of birefringence, the spectral dependence of optic-axes direction, and the linear range of optical response. Within the maximum transmittance band and the linear range of mechanical response the linear range of birefringence is maximum and the dispersion of birefringence is minimum with respect to the shear-strain rate; the corresponding dispersion of optic axis is also minimum. Samples of typical recordings are given in the visible and the infrared radiation for typical flow patterns. One of the practical conclusions is that to optimize the flow-birefringence studies of engineering problems it is advisable to choose the radiation in the near-infrared range. The evidence presented shows that the common trend in engineering research toward simplification of the model of the flow-birefringence response is not necessary.     

Stress state in tempered glass plate and determination of heat-transfer rate

Thermal tempering is widely used to manufacture safety glass for economic as well as for certain safety measures. Laboratory investigations of the tempering process and the resultant strengthening effect are generally limited to rectangular specimens. Results are, therefore, appropriate for this particular geometry. This paper describes a simple stress-state model of a tempered flat glass specimen. the model, developed using photoelastic equations to determine the three-dimensional stress components, was used to predict the transient birefringence in a rectangular glass specimen subjected to uniform and symmetrical heat-transfer conditions, at a temperature where glass behaves as a perfect elastic material with no stress relaxation within the experimental time. A method of determining the coefficient of heat-transfer rate was then developed based on the analysis of the transient birefringence. This technique uses the glass specimen as an optical transducer, and does not affect, in any way, the natural flow of heat by forced convection or contact cooling.     

Photoviscoelasticity on a microsecond time scale

A previous paper¹² has described the optical calibration of photoviscoelastic materials on a microsecond time scale. In this paper, attention is given to the experimental determination of the two-dimensional plane-stress field in a body subjected to arbitrary loads. Symmetry of load and geometry is not assumed. Since the stress state depends on the history of fringe order and isoclinic angle, these basic data must be recorded. Due to nonlinearity in the material studied, the photoviscoelastic data were limited to fractional fringe orders. This introduced problems of initial birefringence and polariscope imperfections. Techniques are described which correct for these imperfections and allow for acquiring and analyzing the basic photoviscoelastic data.     

A microstructure theory of photoelastic behavior in amorphous solids

Available theories to explain the phenomenon of photomechanical behavior in solid materials below the transition temperature are qualitative in nature, and several distinct mechanisms are capable of producing a deformation birefringence. A new mechanism is proposed on the atomic level to account quantitatively for deformation birefringence in an ideal amorphous elastic solid. The material is an isotropic, statistically homogeneous, elastic medium consisting of a random spatial arrangement of heavy mass points (atom nuclei) with positive electric charge in static equilibrium with a corresponding number of continuous, spherical, negatively charged regions (electron clouds). The medium has a nonzero random initial polarization; changes in the components of the dielectric tensor at optical frequencies are computed for infinitesimal uniaxial strain using the Lorentz field approximation for isotropic media. The stress-optical constant is then computed from the associated change in refractive index, and is shown to be in good agreement with experimental values for ordinary photoelastic materials.     

N31型磷酸盐激光玻璃的摩擦磨损性能研究

在Rtec-MFT3000多功能摩擦磨损试验机上采用硅酸盐玻璃球作为对摩副,研究了0.2~2 N的载荷条件下N31型磷酸盐激光玻璃的摩擦磨损性能,着重讨论了载荷对该玻璃摩擦磨损性能的影响.结果显示:稳定磨损阶段的摩擦系数随载荷的增加而减小,且载荷越大摩擦系数达到稳定所需的时间越短.随着载荷的增加,N31型磷酸盐激光玻璃的磨损体积先急剧增加后缓慢增加,同时磨损机理经历从磨粒磨损为主到磨粒磨损和裂纹滋生并存最后到脆性剥落为主的转变过程.而硅酸盐玻璃球的磨损体积在给定载荷范围内随载荷的增加保持线性增加,且在所有试验载荷下的磨损机理均以磨粒磨损为主.在目前试验条件下N31型磷酸盐玻璃表面磨损区域未发生可被EDS检测到的明显的摩擦化学反应,磨屑成分为对摩副两种材料的混合体.     

Effects of initial anisotropy on the finite strain deformation behavior of glassy polymers

Solid phase deformation processing of glassy polymers produces highly anisotropic polymer components as a result of the massive reorientation of molecular chains during the large strain forming operation. Indeed, the polymer preform used as the starting materials is usually anisotropic owing to its prior deformation history. The process end product has often been fashioned for a particular application, i.e. to possess an increased flow strength along a particular axis, thereby exploiting the orientation induced anisotropy effects. The fully three-dimensional issues involved in the use of glassy polymer components include anisotropic flow strenghts, limiting extensibilities, and deformation patterns. These characteristics have been altered by the initial forming operation but are obviously not expected to be enhanced in all directions. The presence of anisotropy in structural components may also lead to premature failure or unexpected shear localization. In this report the effects of initial deformation and the associated anisotropies are investigated through uniaxial compression tests on preoriented polycarbonate (PC) and polymethylmethacrylate (PMMA) specimens. The evolving anisotropy is monitored by testing materials preoriented by various amounts of strain and under different states of deformation. The tensorial nature of the anisotropic material is characterized by examining the preoriented material response in three orthogonal directions. A model for the large strain deformation response of glassy polymers has been shown by Arruda and Boyce [in press] to be well predictive of the evolution of anisotropy during deformation in initially isotropic materials. Here the authors evaluate the ability of the model developed in Arruda and Boyce [in press] to predict several aspects of the anisotropic response of preoriented materials. Using material properties determined from the characterization of the isotropic material response and a knowledge of the anisotropic state of the preoriented material, model simulations are shown to accurately capture all aspects of the large strain anisotropic response including flow strengths, strain hardening characteristics, cross-sectional deformation patterns, and limiting extensibilities. Although anisotropy has been shown to evolve with temperature and strain rate in Boyce, Arruda and Jayachandran [in press] and also state of deformation in Arruda and Boyce [in press], we submit an experimental observation that the subsequent deformation response of preoriented polymers may be predicted using only a measure of optical anisotropy, and not the prior strain or thermal history. Optical anisotropy, as measured for example by birefringence, therefore represents a true internal variable indicative of the evolution of anisotropy with inelastic strain, state of strain, and temperature.     

Thermal contraction and volume relaxation of amorphous polymers

Two experimental techniques are described for the determination of the change of specific volume of polymers with temperature and aging time, which allow measurements between – 160 °C and + 200 °C. Four technical amorphous polymers, PS, PVC, PMMA and PC have been investigated. Volume-temperature curves under constant rate of cooling are presented and interpreted with respect to relaxation processes known from other physical investigations. The rate dependence of dilatometric glass transition temperatures is compared with the time dependence of rheometric glass transition temperatures from shear creep data. Volume relaxation data at constant aging temperature are presented. Aging is found to proceed until very low temperatures in the glassy state for e.g. PMMA.For polystyrene, a comparison is made between the predictions of a very simple theory of volume relaxation due to Kovacs with experimental data, using additional information from volume temperature curves and the time temperature shift of the shear creep transition. The theory predicts a rate of volume relaxation which is much lower than that found by experiment.     

Birefringence measurements in extensional flow of polyisobutylene around an expanding bubble

Birefringence in liquid polymers offers the possibility of obtaining information about stress in complex flows. In this work, this is done for extensional flows of polyisobutylene in a “breathing bubble” rheometer. In this type of rheometer, a bubble consisting of an incompressible, low-viscosity fluid (usually water) is injected into the sample with a nozzle. Expanding or collapsing the bubble by adding or removing water induces biaxial or uniaxial extension in the surrounding sample. The pressure difference between the bubble and the surroundings can be measured and compared to the predictions of constitutive equations. This measurement only gives one integral value for a complex flow history. In this paper, the birefringence around the bubble is measured in order to learn more about the flow. This is done by comparing pressure and birefringence results to those of standard constitutive equations for a polyisobutylene sample. A good agreement between the pressure and optical measurements and the theory is found with a single value of the stress-optical constant. Received: 25 June 1997 Accepted: 12 November 1997     

A stress-optic law for photoelastic analysis of orthotropic composites

The feasibility for utilizing transparent filament-resin composites for photoelastic stress analysis was investigated. Satisfactory photoelastic stress patterns were demonstrated in simple models with undirectional and bidirectional fiber orientations. A stress-optic law was formulated, based on the concept that the birefringence components contributed by each component of plane stress are combined according to a Mohr circle of birefringence. Applying this concept, the difference of the physical and optical principal directions was accounted for, and a general method of photoelastic solution for the plane-stress problem in orthotropic sheets was developed. The method of analysis is little more complex than the well-known procedures for isotropic materials, but at least three experimental measurements are required to characterize the optical response of the material to plane stress. Partial confirmation of the proposed stress-optic law was obtained by comparison of the theory to limited experimental data obtained in uniaxial-stress samples. It remains to establish a more positive verification by experiments in a variety of biaxial-stress conditions.     

Application of the GIMP software in the analysis of birefringence images obtained in a multipass rheometer

Flow-induced birefringence is a technique with numerous potential applications in polymers, because the bright and dark fringe patterns of the birefringence images can be related to principal stress difference (PSD) profile along the flow centerline. In this work, we developed an easy-to-use methodology for birefringence image processing using the GIMP open-source software. In order to illustrate its application, images obtained in previous work during the flow of two grades of general purpose polystyrene through the slit-die geometry in the multipass rheometer MPR4, located at the University of ?Cambridge, UK, were reprocessed. The results showed that the PSD module profile along the flow centerline obtained with the proposed methodology is more accurate than the manual technique and is obtained with shorter processing time.     

Tricolor photoviscoelastic technique and its application to moving contact

A new technique for simultaneous determination of both fringe order and principal direction of birefringence in practical photoviscoelastic analysis using white incident light with a set of the primary colors, called tricolor photoviscoelasticity, is described. This method can determine both the fringe order and principal direction of birefringence from a single-color photoviscoelastic image under plane polarization. Then, the authors evaluate time dependent stresses and strains around a contact region in a viscoelastic strip plate under nonproportional loading condition. The variations of the principal stresses and strains are easily obtained over a wide time range by use of the optical constitutive equations of photoviscoelasticity and the characteristic material property functions.     

Rheo-optical investigations of lyotropic mesophases of polymeric surfactants

The shear orientation of hexagonal and lamellar liquid crystalline phases of polymeric surfactants was investigated by rheo-optical techniques (flow birefringence (Δn), small-angle light scattering) as well as by nuclear magnetic resonance and optical microscopy. The evolution of birefringence in the hexagonal phase is discussed for simple and oscillatory shear, and an alignment of rodlike micelles along the flow direction was found. A shear induced formation of vesicles (“onions”) is observed with the lamellar phase. They displayed a characteristic four-lobe pattern in depolarized light scattering. Above a critical shear stress vesicles were degraded and perpendicularly aligned lamellae (i.e. with their normal along the vorticity direction) were obtained. A comparison of experiments performed at constant stress and constant rate revealed that the vesicle to planar lamellae transition occurred above a critical shear stress. The behavior of the polysoap lyotropic mesophases under shear, i.e. the strain dependent alignment in the hexagonal phase, the shear induced formation of vesicles, and a transition to planar lamellae in the lamellar phase, is very similar to the behavior of lyotropic mesophases formed by low molar mass surfactants or amphiphilic block copolymers. The geometrical constraints that are introduced when amphiphilic side groups are fixed to a polymer backbone do not significantly alter the response of the mesophase to a shear deformation. Received: 4 May 1999 /Accepted: 19 July 1999     

Finite amplitude, free vibrations of an axisymmetric load supported by a highly elastic tubular shear spring

The finite amplitude, free vibrational characteristics of a simple mechanical system consisting of an axisymmetric rigid body supported by a highly elastic tubular shear spring subjected to axial, rotational, and coupled shearing motions are studied. Two classes of elastic tube materials are considered: a compressible material whose shear response is constant, and an incompressible material whose shear response is a quadratic function of the total amount of shear. The class of materials with constant shear response includes the incompressible Mooney-Rivlin material and certain compressible Blatz-Ko, Hadamard, and other general kinds of models. For each material class, the quasi-static elasticity problem is solved to determine the telescopic and gyratory shearing deformation functions needed to evaluate the elastic tube restoring force and torque exerted on the body. For all materials with constant shear response, the differential equations of motion are uncoupled equations typical of simple harmonic oscillators. Hence, exact solutions for the forced vibration of the system can be readily obtained; and for this class, engineering design formulae for the load-deflection relations are discussed and compared with experimental results of others'. For the quadratic material, however, the general motion of the body is characterized by a formidable, coupled system of nonlinear equations. The free, coupled shearing motion for which either the axial or the azimuthal shear deformation may be small is governed by a pair of equations of the Duffing and Hill types. On the other hand, the finite amplitude, pure axial and pure rotational motions of the load are described by the classical, nonlinear Duffing equation alone. A variety of problems are solved exactly for these separate free vibrational modes, and a number of physical results are presented throughout.     

Ageing and rejuvenation in glassy amorphous polymers

Physical ageing of amorphous polymers well below their glass transition temperature leads to changes in almost all physical properties. Of particular interest is the increase in yield stress and post-yield strain softening that accompanies ageing of these materials. Moreover, at larger strain polymers seem to rejuvenate, i.e. aged and non-aged samples have identical stress-strain responses. Also, plastically deforming an aged sample seems to rejuvenate the polymer. In this work we use molecular dynamic simulations with a detailed force field suitable for macromolecular ensembles to simulate and understand the effects of ageing on the mechanical response of these materials. We show that within the timescales of these simulations it is possible to simulate both ageing and rejuvenation. The short range potentials play an important role in ageing and rejuvenation. A typical yield drop exhibited by glassy polymers is a manifestation of a sudden relaxation in the short range structure of an aged polymer. Moreover, the aged polymers are known to be brittle. We show that this is intimately related to its typical stress-strain response which allows it to carry arbitrarily large mean stresses ahead of a notch.     

Orientation dynamics in commercial thermotropic liquid crystalline polymers in transient shear flows

In situ X-ray scattering measurements of molecular orientation under shear are reported for two commercial thermotropic liquid crystalline polymers (TLCPs), Vectra A950® and Vectra B950®. Transient shear flow protocols (reversals, step changes, and flow cessation) are used to investigate the underlying director dynamics. Synchrotron X-ray scattering in conjunction with a high-speed area detector provides sufficient time resolution to limit the total time spent in the melt during testing, whereas a redesigned X-ray capable shear cell provides a more robust platform for working with TLCP melts at high temperatures. The transient orientation response upon flow inception or flow reversal does not provide definitive signatures of either tumbling or shear alignment. However, the observation of clear transient responses to step increases or step decreases in shear rate contrasts with expectations and experience with shear-aligning nematics and suggests that these polymers are of the tumbling class. Finally, these two polymers show opposite trends in orientation following flow cessation, which appears to correlate with the evolution of dynamic modulus during relaxation. Specifically, Vectra B shows an increase in orientation upon flow cessation, an observation that can only be rationalized by the assumption of tumbling dynamics in shear. Together with prior observations of commercial LCP melts in channel flows, these results suggest that this class of materials, as a rule, exhibits director tumbling.     

Birefringence measurements on polymer melts in an axisymmetric flow cell

 The stress-optical rule relates birefringence to stress. Consequently, measurement of flow birefringence provides a non-intrusive technique of measuring stresses in complex flows. In this investigation we explore the use of an axisymmetric geometry to create a uniaxial elongational flow in polymer melts. In axisymmetric flows both birefringence and orientation angle change continuously along the path of the propagating light. The cumulative influence of the material's optical properties along the light's integrated path makes determination of local birefringence in the melt impossible. One can nevertheless use birefringence measurements to compare with predictions from computer simulations as a means of evaluating the constitutive equations for the stress. More specifically, in this investigation we compare the light intensity transmitted through the experimental set-up vs entry position, with the theoretically calculated transmitted intensity distribution as a means of comparing experiment and simulation. The main complication in our experiments is the use of a flow cell that necessarily consists of materials of different refractive indices. This introduces refraction and reflection effects that must be modeled before experimental results can be correctly interpreted. We describe how these effects are taken into account and test the accuracy of predictions against experiments. In addition, the high temperatures required to investigate polymer melts mean that a further complication is introduced by thermal stresses present in the flow cell glass. We describe how these thermal-stresses are also incorporated in the simulations. Finally, we present some preliminary results and evaluate the success of the overall method. Received: 2 April 2001 Accepted: 27 August 2001     

Temperature and time influence in the stress freezing of the epoxy Hysol 4290

Disks of the photoelastic epoxy known as Hysol 4290 have been subjected to constant load at various temperature levels and the birefringence has been recorded as time elapsed (creep test). Also disks of the same material were loaded at the critical temperature and then cooled, each to a different temperature level and, after they reached thermal equilibrium, the loading was removed while the temperature was maintained constant (recovery test). The effect of time on the fringe value is given for both groups of tests using the temperature as a parameter. Finally, tensile specimens have been subjected to various loads at the critical temperature and fringe response and failure recorded. The results obtained may be useful for the design of experiments and, in some cases, to shorten the time required to conduct a three-dimensional photoelasticity investigation using the “freezing” method.